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Restrict all autos to one subgoal.

This commit is contained in:
Michael Herzberg 2020-07-16 09:04:34 +01:00
parent cebefb53dc
commit 99a6566ed0
6 changed files with 59 additions and 48 deletions
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7
Core_DOM/Core_DOM/common/Core_DOM_Functions.thy
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@ -216,7 +216,7 @@ lemma get_child_nodes_reads: "reads (get_child_nodes_locs ptr) (get_child_nodes
intro!: reads_bind_pure reads_subset[OF return_reads] )[1]
apply(auto simp add: get_child_nodes\<^sub>e\<^sub>l\<^sub>e\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def intro: reads_subset[OF reads_singleton]
reads_subset[OF check_in_heap_reads] intro!: reads_bind_pure reads_subset[OF return_reads]
split: option.splits)
split: option.splits)[1]
done
end
@ -618,7 +618,8 @@ lemma set_child_nodes_get_child_nodes_different_pointers:
apply(auto)[1]
apply(auto)[1]
apply(rule is_element_ptr_kind_obtains)
apply(auto)
apply(auto)[1]
apply(auto)[1]
done
lemma set_child_nodes_element_ok [simp]:
@ -668,7 +669,7 @@ proof -
by(auto simp add: known_ptr_impl known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
then show ?thesis
using assms
apply(auto simp add: set_child_nodes_def a_set_child_nodes_tups_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)
apply(auto simp add: set_child_nodes_def a_set_child_nodes_tups_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def)[1]
apply(split invoke_splits, rule conjI)+
apply(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]
apply(auto simp add: is_element_ptr_kind\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def set_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def split: option.splits)[1]

2
Core_DOM/Core_DOM/common/monads/CharacterDataMonad.thy
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@ -308,7 +308,7 @@ lemma type_wf_put_ptr_not_in_heap_E:
shows "type_wf h"
using assms
apply(auto simp add: type_wf_defs elim!: ElementMonad.type_wf_put_ptr_not_in_heap_E
split: option.splits if_splits)
split: option.splits if_splits)[1]
using assms(2) node_ptr_kinds_commutes by blast
lemma type_wf_put_ptr_in_heap_E:

2
Core_DOM/Core_DOM/common/monads/DocumentMonad.thy
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@ -498,7 +498,7 @@ lemma put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_doct
apply(auto simp add: is_document_kind_def type_wf_defs ElementClass.type_wf_defs
NodeClass.type_wf_defs ElementMonad.get_M_defs ObjectClass.type_wf_defs
CharacterDataClass.type_wf_defs split: option.splits)[1]
apply(auto simp add: get_M_defs)
apply(auto simp add: get_M_defs)[1]
by (metis (mono_tags) error_returns_result finite_set_in option.exhaust_sel option.simps(4))
lemma put_M\<^sub>D\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t_document_element_type_wf_preserved [simp]:

4
Core_DOM/Core_DOM/common/monads/NodeMonad.thy
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@ -165,7 +165,7 @@ lemma type_wf_put_ptr_in_heap_E:
assumes "is_node_ptr_kind ptr \<Longrightarrow> is_node_kind (the (get ptr h))"
shows "type_wf h"
using assms
apply(auto simp add: type_wf_defs split: option.splits if_splits)
apply(auto simp add: type_wf_defs split: option.splits if_splits)[1]
by (metis ObjectClass.get\<^sub>O\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t_type_wf bind.bind_lunit finite_set_in get\<^sub>N\<^sub>o\<^sub>d\<^sub>e_def is_node_kind_def option.exhaust_sel)
@ -192,7 +192,7 @@ lemma type_wf_preserved_small:
assumes "\<And>node_ptr. preserved (get_M\<^sub>N\<^sub>o\<^sub>d\<^sub>e node_ptr RNode.nothing) h h'"
shows "type_wf h = type_wf h'"
using type_wf_preserved allI[OF assms(2), of id, simplified]
apply(auto simp add: type_wf_defs)
apply(auto simp add: type_wf_defs)[1]
apply(auto simp add: preserved_def get_M_defs node_ptr_kinds_small[OF assms(1)]
split: option.splits)[1]
apply (metis notin_fset option.simps(3))

61
Core_DOM/Core_DOM/standard/Core_DOM_Heap_WF.thy
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@ -1492,7 +1492,7 @@ proof -
apply(rule bind_cong_2)
apply(auto intro!: filter_M_pure_I bind_pure_I)[1]
apply(auto intro!: filter_M_pure_I bind_pure_I)[1]
apply(auto simp add: filter_eq (* dest!: returns_result_eq[OF ptrs] *))
apply(auto simp add: filter_eq (* dest!: returns_result_eq[OF ptrs] *))[1]
using filter_eq ptrs apply auto[1]
using filter_eq ptrs by auto
qed
@ -2808,7 +2808,11 @@ next
then have "some_owner_document \<in> set candidates"
apply(rule filter_M_in_result_if_ok)
using \<open>some_owner_document |\<in>| document_ptr_kinds h\<close> \<open>root \<in> cast ` set |h \<turnstile> get_disconnected_nodes some_owner_document|\<^sub>r\<close>
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)[1]
using \<open>some_owner_document |\<in>| document_ptr_kinds h\<close> \<open>root \<in> cast ` set |h \<turnstile> get_disconnected_nodes some_owner_document|\<^sub>r\<close>
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)[1]
using \<open>some_owner_document |\<in>| document_ptr_kinds h\<close> \<open>root \<in> cast ` set |h \<turnstile> get_disconnected_nodes some_owner_document|\<^sub>r\<close>
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)[1]
by (simp add: "1" local.get_disconnected_nodes_ok)
then have "candidates \<noteq> []"
@ -2915,7 +2919,7 @@ proof -
by (meson bind_pure_returns_result_I bind_returns_result_E3 local.get_root_node_pure)
then show ?thesis
using \<open>known_ptr ptr\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def known_ptr_impl)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def known_ptr_impl)[1]
apply(split invoke_splits, ((rule conjI | rule impI)+)?)+
apply(drule(1) known_ptr_not_document_ptr[folded known_ptr_impl])
apply(drule(1) known_ptr_not_character_data_ptr)
@ -3038,7 +3042,7 @@ proof -
assume "is_node_ptr_kind ptr"
then have ?thesis
using \<open>known_ptr ptr\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close>
apply(auto simp add: known_ptr_impl get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: known_ptr_impl get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
apply(drule(1) known_ptr_not_document_ptr[folded known_ptr_impl])
apply(drule(1) known_ptr_not_character_data_ptr)
@ -3104,7 +3108,7 @@ proof -
using True
by (smt \<open>h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document\<close> assms(1) assms(2) assms(3) assms(4) document_ptr_casts_commute3 get_root_node_document returns_result_eq)
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using \<open>is_document_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r root\<close> apply blast
using \<open>root |\<in>| object_ptr_kinds h\<close>
@ -3119,14 +3123,15 @@ proof -
by (metis node_ptr_casts_commute3)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r root_node_ptr () \<rightarrow>\<^sub>r owner_document"
using \<open>h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr () \<rightarrow>\<^sub>r owner_document\<close> assms(4)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)[1]
apply (metis assms(1) assms(2) assms(3) local.get_root_node_no_parent local.get_root_node_same_no_parent node_ptr returns_result_eq)
using \<open>is_node_ptr_kind root\<close> node_ptr returns_result_eq by fastforce
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using \<open>is_node_ptr_kind root\<close> \<open>known_ptr root\<close>
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[2]
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[1]
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[1]
using \<open>root |\<in>| object_ptr_kinds h\<close>
by(auto simp add: root_node_ptr)
qed
@ -3137,10 +3142,10 @@ proof -
case True
have "root = cast owner_document"
using \<open>h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits)+
apply (meson invoke_empty is_OK_returns_result_I)
apply(auto simp add: True a_get_owner_document\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: if_splits)
apply(auto simp add: True a_get_owner_document\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: if_splits)[1]
apply (metis True cast_document_ptr_not_node_ptr(2) is_document_ptr_kind_obtains is_node_ptr_kind_none node_ptr_casts_commute3 option.case_eq_if)
by (metis True cast_document_ptr_not_node_ptr(1) document_ptr_casts_commute3 is_node_ptr_kind_none node_ptr_casts_commute3 option.case_eq_if)
then show ?thesis
@ -3155,16 +3160,16 @@ proof -
by (metis node_ptr_casts_commute3)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r root_node_ptr () \<rightarrow>\<^sub>r owner_document"
using \<open>h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits)+
apply (meson invoke_empty is_OK_returns_result_I)
by(auto simp add: is_document_ptr_kind_none elim!: bind_returns_result_E2)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr () \<rightarrow>\<^sub>r owner_document"
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)[1]
using assms(1) assms(2) assms(3) assms(4) local.get_root_node_no_parent local.get_root_node_same_no_parent node_ptr returns_result_eq root_node_ptr
by fastforce+
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using node_ptr \<open>known_ptr ptr\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close>
@ -3185,7 +3190,7 @@ locale l_get_owner_document_wf_get_root_node_wf = l_heap_is_wellformed_defs + l_
lemma get_owner_document_wf_get_root_node_wf_is_l_get_owner_document_wf_get_root_node_wf [instances]:
"l_get_owner_document_wf_get_root_node_wf heap_is_wellformed type_wf known_ptr known_ptrs get_root_node get_owner_document"
apply(auto simp add: l_get_owner_document_wf_get_root_node_wf_def l_get_owner_document_wf_get_root_node_wf_axioms_def instances)
apply(auto simp add: l_get_owner_document_wf_get_root_node_wf_def l_get_owner_document_wf_get_root_node_wf_axioms_def instances)[1]
using get_root_node_document apply blast
using get_root_node_same_owner_document apply (blast, blast)
done
@ -6097,7 +6102,7 @@ proof -
using assms(2) assms(4) local.known_ptrs_known_ptr node_ptr_kinds_commutes by blast
then show ?thesis
using assms
apply(auto simp add: a_next_sibling_def intro!: bind_is_OK_pure_I split: option.splits list.splits)
apply(auto simp add: a_next_sibling_def intro!: bind_is_OK_pure_I split: option.splits list.splits)[1]
using get_child_nodes_ok local.get_parent_parent_in_heap local.known_ptrs_known_ptr by blast
qed
@ -6133,7 +6138,7 @@ proof -
using \<open>ptr |\<in>| object_ptr_kinds h\<close>
apply(simp add: get_child_nodes_def a_get_child_nodes_tups_def)
apply(split invoke_splits)+
apply(auto split: option.splits)
apply(auto split: option.splits)[1]
apply (meson invoke_empty is_OK_returns_result_I)
apply (meson invoke_empty is_OK_returns_result_I)
by(auto simp add: get_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: option.splits)
@ -6181,13 +6186,15 @@ proof -
by(auto simp add: known_ptr_impl known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)
ultimately show ?thesis
using assms(4)
apply(auto simp add: get_child_nodes_def a_get_child_nodes_tups_def)
apply(auto simp add: get_child_nodes_def a_get_child_nodes_tups_def)[1]
apply(split invoke_splits)+
apply(auto elim!: bind_returns_result_E2 split: option.splits)
apply(auto simp add: get_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: option.splits)
using \<open>ptr |\<in>| object_ptr_kinds h\<close> \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>object_ptr_kinds h = object_ptr_kinds h2\<close> \<open>type_wf h2\<close> assms(4) local.set_child_nodes_document1_ok apply blast
using \<open>ptr |\<in>| object_ptr_kinds h\<close> \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>object_ptr_kinds h = object_ptr_kinds h2\<close> \<open>type_wf h2\<close> assms(4) local.set_child_nodes_document1_ok apply blast
using \<open>ptr |\<in>| object_ptr_kinds h\<close> \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>object_ptr_kinds h = object_ptr_kinds h2\<close> \<open>type_wf h2\<close> assms(4) is_element_ptr_kind_cast local.set_child_nodes_document2_ok by blast
apply(auto elim!: bind_returns_result_E2 split: option.splits)[1]
apply(auto simp add: get_child_nodes\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: option.splits)[1]
using assms(5) apply auto[1]
using \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>object_ptr_kinds h = object_ptr_kinds h2\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close> \<open>type_wf h2\<close> local.set_child_nodes_document1_ok apply blast
using \<open>is_document_ptr_kind ptr\<close> \<open>known_ptr ptr\<close> \<open>object_ptr_kinds h = object_ptr_kinds h2\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close> \<open>type_wf h2\<close> is_element_ptr_kind_cast local.set_child_nodes_document2_ok apply blast
using \<open>\<not> is_character_data_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ptr\<close> apply blast
by (metis False is_element_ptr_implies_kind option.case_eq_if)
qed
then
obtain h' where
@ -6203,7 +6210,7 @@ proof -
bind_is_OK_pure_I[OF get_disconnected_nodes_pure]
bind_is_OK_I[rotated, OF h2]
dest!: returns_result_eq[OF assms(4)] returns_result_eq[OF owner_document] returns_result_eq[OF disconnected_nodes_h]
)
)[1]
using h2 returns_result_select_result by force
qed
@ -6345,7 +6352,7 @@ proof -
using \<open>h2 \<turnstile> ok get_disconnected_nodes old_document\<close>
using \<open>h3 \<turnstile> ok get_disconnected_nodes document_ptr\<close>
apply(auto dest!: returns_result_eq[OF old_disc_nodes] returns_result_eq[OF disc_nodes]
intro!: bind_is_OK_I[rotated, OF h3] bind_is_OK_pure_I[OF get_disconnected_nodes_pure] )
intro!: bind_is_OK_I[rotated, OF h3] bind_is_OK_pure_I[OF get_disconnected_nodes_pure] )[1]
using \<open>h2 \<turnstile> ok set_disconnected_nodes old_document (remove1 child old_disc_nodes)\<close> by auto
qed
then obtain h' where
@ -6368,7 +6375,7 @@ proof -
intro!: bind_is_OK_pure_I[OF get_owner_document_pure]
bind_is_OK_pure_I[OF get_parent_pure]
bind_is_OK_I[rotated, OF h2]
dest!: returns_result_eq[OF parent_opt] returns_result_eq[OF old_document])
dest!: returns_result_eq[OF parent_opt] returns_result_eq[OF old_document])[1]
using \<open>h \<turnstile> ok (case parent_opt of None \<Rightarrow> return () | Some parent \<Rightarrow> remove_child parent child)\<close>
by auto
qed
@ -6514,7 +6521,7 @@ proof -
bind_is_OK_pure_I[OF get_disconnected_nodes_pure]
dest!: returns_result_eq[OF owner_document] returns_result_eq[OF disconnected_nodes_h2] returns_heap_eq[OF h2] returns_heap_eq[OF h3]
dest!: sym[of node ref]
)
)[1]
using returns_result_eq by fastforce
qed
end
@ -7146,7 +7153,7 @@ proof -
bind_returns_heap_E2[rotated, OF get_disconnected_nodes_pure, rotated] )
then
have "h \<turnstile> create_character_data document_ptr text \<rightarrow>\<^sub>r new_character_data_ptr"
apply(auto simp add: create_character_data_def intro!: bind_returns_result_I)
apply(auto simp add: create_character_data_def intro!: bind_returns_result_I)[1]
apply (metis is_OK_returns_heap_I is_OK_returns_result_E old.unit.exhaust)
apply (metis is_OK_returns_heap_E is_OK_returns_result_I local.get_disconnected_nodes_pure pure_returns_heap_eq)
by (metis is_OK_returns_heap_I is_OK_returns_result_E old.unit.exhaust)

31
Core_DOM/Core_SC_DOM/safely_composable/Core_DOM_Heap_WF.thy
View File

@ -1492,7 +1492,7 @@ proof -
apply(rule bind_cong_2)
apply(auto intro!: filter_M_pure_I bind_pure_I)[1]
apply(auto intro!: filter_M_pure_I bind_pure_I)[1]
apply(auto simp add: filter_eq (* dest!: returns_result_eq[OF ptrs] *))
apply(auto simp add: filter_eq (* dest!: returns_result_eq[OF ptrs] *))[1]
using filter_eq ptrs apply auto[1]
using filter_eq ptrs by auto
qed
@ -2808,8 +2808,10 @@ next
then have "some_owner_document \<in> set candidates"
apply(rule filter_M_in_result_if_ok)
using \<open>some_owner_document |\<in>| document_ptr_kinds h\<close> \<open>root \<in> cast ` set |h \<turnstile> get_disconnected_nodes some_owner_document|\<^sub>r\<close>
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)
by (simp add: "1" local.get_disconnected_nodes_ok)
apply(auto intro!: bind_pure_I bind_pure_returns_result_I)[1]
apply (simp add: \<open>some_owner_document |\<in>| document_ptr_kinds h\<close>)
using "1" \<open>root \<in> cast\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r\<^sub>2\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r ` set |h \<turnstile> get_disconnected_nodes some_owner_document|\<^sub>r\<close> \<open>some_owner_document |\<in>| document_ptr_kinds h\<close> local.get_disconnected_nodes_ok
by auto
then have "candidates \<noteq> []"
by auto
@ -2915,7 +2917,7 @@ proof -
by (meson bind_pure_returns_result_I bind_returns_result_E3 local.get_root_node_pure)
then show ?thesis
using \<open>known_ptr ptr\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def known_ptr_impl)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def known_ptr_impl)[1]
apply(split invoke_splits, ((rule conjI | rule impI)+)?)+
apply(drule(1) known_ptr_not_document_ptr[folded known_ptr_impl])
apply(drule(1) known_ptr_not_character_data_ptr)
@ -3107,7 +3109,7 @@ proof -
using True
by (smt \<open>h \<turnstile> get_owner_document ptr \<rightarrow>\<^sub>r owner_document\<close> assms(1) assms(2) assms(3) assms(4) document_ptr_casts_commute3 get_root_node_document returns_result_eq)
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using \<open>is_document_ptr\<^sub>o\<^sub>b\<^sub>j\<^sub>e\<^sub>c\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r root\<close> apply blast
using \<open>root |\<in>| object_ptr_kinds h\<close>
@ -3122,14 +3124,15 @@ proof -
by (metis node_ptr_casts_commute3)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r root_node_ptr () \<rightarrow>\<^sub>r owner_document"
using \<open>h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr () \<rightarrow>\<^sub>r owner_document\<close> assms(4)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)[1]
apply (metis assms(1) assms(2) assms(3) local.get_root_node_no_parent local.get_root_node_same_no_parent node_ptr returns_result_eq)
using \<open>is_node_ptr_kind root\<close> node_ptr returns_result_eq by fastforce
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using \<open>is_node_ptr_kind root\<close> \<open>known_ptr root\<close>
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[2]
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[1]
apply(auto simp add: known_ptr_impl DocumentClass.known_ptr_defs CharacterDataClass.known_ptr_defs ElementClass.known_ptr_defs NodeClass.known_ptr_defs split: option.splits)[1]
using \<open>root |\<in>| object_ptr_kinds h\<close>
by(auto simp add: root_node_ptr)
qed
@ -3140,10 +3143,10 @@ proof -
case True
have "root = cast owner_document"
using \<open>h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits)+
apply (meson invoke_empty is_OK_returns_result_I)
apply(auto simp add: True a_get_owner_document\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: if_splits)
apply(auto simp add: True a_get_owner_document\<^sub>d\<^sub>o\<^sub>c\<^sub>u\<^sub>m\<^sub>e\<^sub>n\<^sub>t\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 split: if_splits)[1]
apply (metis True cast_document_ptr_not_node_ptr(2) is_document_ptr_kind_obtains is_node_ptr_kind_none node_ptr_casts_commute3 option.case_eq_if)
by (metis True cast_document_ptr_not_node_ptr(1) document_ptr_casts_commute3 is_node_ptr_kind_none node_ptr_casts_commute3 option.case_eq_if)
then show ?thesis
@ -3158,16 +3161,16 @@ proof -
by (metis node_ptr_casts_commute3)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r root_node_ptr () \<rightarrow>\<^sub>r owner_document"
using \<open>h \<turnstile> get_owner_document root \<rightarrow>\<^sub>r owner_document\<close>
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits)+
apply (meson invoke_empty is_OK_returns_result_I)
by(auto simp add: is_document_ptr_kind_none elim!: bind_returns_result_E2)
then have "h \<turnstile> local.a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r node_ptr () \<rightarrow>\<^sub>r owner_document"
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)
apply(auto simp add: a_get_owner_document\<^sub>n\<^sub>o\<^sub>d\<^sub>e\<^sub>_\<^sub>p\<^sub>t\<^sub>r_def elim!: bind_returns_result_E2 intro!: bind_pure_returns_result_I filter_M_pure_I bind_pure_I split: option.splits)[1]
using assms(1) assms(2) assms(3) assms(4) local.get_root_node_no_parent local.get_root_node_same_no_parent node_ptr returns_result_eq root_node_ptr
by fastforce+
then show ?thesis
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)
apply(auto simp add: get_owner_document_def a_get_owner_document_tups_def)[1]
apply(split invoke_splits, (rule conjI | rule impI)+)+
using node_ptr \<open>known_ptr ptr\<close> \<open>ptr |\<in>| object_ptr_kinds h\<close>
@ -3188,7 +3191,7 @@ locale l_get_owner_document_wf_get_root_node_wf = l_heap_is_wellformed_defs + l_
lemma get_owner_document_wf_get_root_node_wf_is_l_get_owner_document_wf_get_root_node_wf [instances]:
"l_get_owner_document_wf_get_root_node_wf heap_is_wellformed type_wf known_ptr known_ptrs get_root_node get_owner_document"
apply(auto simp add: l_get_owner_document_wf_get_root_node_wf_def l_get_owner_document_wf_get_root_node_wf_axioms_def instances)
apply(auto simp add: l_get_owner_document_wf_get_root_node_wf_def l_get_owner_document_wf_get_root_node_wf_axioms_def instances)[1]
using get_root_node_document apply blast
using get_root_node_same_owner_document apply (blast, blast)
done